Source: wikibot/pompeiu-s-theorem
= Pompeiu's theorem
{wiki=Pompeiu's_theorem}
Pompeiu's theorem is a geometric result concerning the relationships between geometric shapes and their properties. Specifically, it states that if \\( S \\) is a bounded measurable set in the Euclidean space \\( \\mathbb\{R\}^n \\), and if \\( f: \\mathbb\{R\}^n \\to \\mathbb\{R\} \\) is a continuous function such that the integral of \\( f \\) over \\( S \\) is zero (i.e.